Math Help: Fractals

Factual Questions
1

I participate on another message board and a fellow there is asking for help that is WAY beyond me and (apparently) most people there. He claims it is not for school credit although it does look like coursework if that changes your mind on helping.

Here is a link to the other forum thread.

Here is a link to the math problem (I’d retype it here but he posted it as an image).

Also from his thread here is a link to the shape after 4 iterations (presumably that helps somehow).

I occasionally sing the praises of the SDMB over there and this will be another one to maybe garner some new recruits. Post on the other board if you can or here and I will copy the answer over with links back to here and (of course) appropriate attribution.

Thanks!

2

I haven’t done this kind of math for a lo-o-ong time but here is a link to the Wikipedia article containing the image you linked, which I could not view from your link.

3

And this year’s award for best linkage goes to… :wink:

4

I know exactly the fractal image he is constructing, however it has been a really long time for me. I do not remember what compact means, and my fractals textbook has gone AWOL. Maybe if you remind me what compact is I can help.

ETA: now that I see the link, I am probably of no use since you all have the same info I do.

5

See here for a definition of compactness and some other properties that might be helpful. The fractal in question is the Koch snowflake.

6

Oh crap :rolleyes: :smack:

7

Thanks for the links so far. I will copy them to the other thread. In case some cannot read the other thread his problem with the question I linked is the final bit (quoted below):

“I’ve done everything up until the last part. It’s just the bit asking whether the limiting shape is compact or not that has me stumped. Any ideas?”

While an answer of which it is would be fine I am guessing he is looking for proof of why it is one or the other.

8

See here for a discussion that contains the answer.